Sums of Independent Random Variables

  • Jiming Jiang
Part of the Springer Texts in Statistics book series (STS, volume 0)


The classical large-sample theory is about the sum of independent random variables. Even though large-sample techniques have expanded well beyond the classical theory, the foundation set up by the latter remains the best way to understand and further explore elements of large-sample theory. Furthermore, the classical results are often used as examples to illustrate more sophisticated theory, as we have done repeatedly so far in this book, and the “gold standard“ for any extensions beyond the classical situation. Here, by gold standard it means that a well-developed, nonclassical large-sample theory should include the classical one as a special case.


Convergence Rate Central Limit Theorem Independent Random Variable Invariance Principle Iterate Logarithm 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of CaliforniaDavisUSA

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